The whole point of Adamantium is that once it is set, only cosmic-level powers (Molecule Man, Thanos, Thor, Serpent, Beyonder-Doom), particle beams and fundamental forces (like magnetism) can alter its shape. It cannot even cut itself. Even an Adamantium bullet cannot break Logan's hard head.

Even under normal circumstances, someone encased in steel could not cut his way out with steel, unless it was a powertool. Sufficient force would need to be supplied, and it couldn't be from the inside.

Hmm, then unless Wolverine now has superhuman strength he shouldn't have been able to cut his way out.

So how is he back? Well he seems to be tasked with obtaining and guarding the mind gemstone, which as I recall was the one that Xavier guarded as part of the Marvel illuminati.

The gems have always been able to tap cosmic energies outside their specialized function, so the gem could have revived and empowered him to carve his way out so that he could find it.

Kobik could have revived him or warped reality so that he wasn't dead.

Perhaps he wasn't dead at all, his healing factor was offline due to some parasitic infection as I recall. So when he was coated in the metal he did perish but before brain death, his body shut down killed the infection and his healing powers rebooted and were restoring him and kept him in stasis-lock until he was freed from the metal. Perhaps his healing power super charged his strength to break free, or since the Phoenix/Adult Jean is coming back and since Jean has always had feelings for Logan perhaps the Phoenix restored Wolverine and the phoenix energy in him blasted his way out of the metal.

Perhaps a clone body created by Sinister, bones and claws coated with the metal and his mind transferred into it.

Perhaps the Weapon X program revived him?

I'm leaning towards the Phoenix Force reviving him or his healing power came back online and kept him in stasis-lock while he healed.

Or it is magic, they don't have to explain it or the Mephisto Mindwipe.